Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/202.jpg" pagenum="174"/>
                    <arrow.to.target n="note150"/>
                  æqualitatis. </s>
                  <s>Attractiones igitur, in contrarias partes æqualiter fac­
                    <lb/>
                  tæ, ſe mutuo deſtruunt. </s>
                  <s>Et ſimili argumento, attractiones omnes
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                  per totam Sphæricam ſuperficiem a contrariis attractionibus de­
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                  ſtruuntur. </s>
                  <s>Proinde corpus
                    <emph type="italics"/>
                  P
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                  nullam in partem his attractionibus
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                  impellitur.
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                  Q.E.D.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note150"/>
                  DE MOTU
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                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXI. THEOREMA XXXI.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Iiſdem poſitis, dico quod corpuſculum extra Sphæricam ſuperficiem
                    <lb/>
                  conſtitutum attrahitur ad centrum Sphæræ, vi reciproce propor­
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                  tionali quadrato diſtantiæ ſuæ ab eodem centro.
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                  </s>
                </p>
                <p type="main">
                  <s>Sint
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                  AHKB, ahkb
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                  æquales duæ ſuperficies Sphæricæ, centris
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                    <emph type="italics"/>
                  S, s,
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                  diametris
                    <emph type="italics"/>
                  AB, ab
                    <emph.end type="italics"/>
                  deſcriptæ, &
                    <emph type="italics"/>
                  P, p
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                  corpuſcula ſita extrin­
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                  ſecus in diametris illis productis. </s>
                  <s>Agantur a corpuſculis lineæ
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                    <figure id="id.039.01.202.1.jpg" xlink:href="039/01/202/1.jpg" number="115"/>
                    <lb/>
                    <emph type="italics"/>
                  PHK, PIL, phk, pil,
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                  auferentes a circulis maximis
                    <emph type="italics"/>
                  AHB,
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                  ahb,
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                  æquales arcus
                    <emph type="italics"/>
                  HK, hk
                    <emph.end type="italics"/>
                  &
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                  IL, il:
                    <emph.end type="italics"/>
                  Et ad eas de­
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                  mittantur perpendicula
                    <emph type="italics"/>
                  SD, sd; SE, se; IR, ir;
                    <emph.end type="italics"/>
                  quorum
                    <lb/>
                    <emph type="italics"/>
                  SD, sd
                    <emph.end type="italics"/>
                  ſecent
                    <emph type="italics"/>
                  PL, pl
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  &
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                  f:
                    <emph.end type="italics"/>
                  Demittantur etiam ad diame­
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                  tros perpendicula
                    <emph type="italics"/>
                  IQ,
                    <expan abbr="iq.">ique</expan>
                    <emph.end type="italics"/>
                  Evaneſcant anguli
                    <emph type="italics"/>
                  DPE, dpe:
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  (ob æquales
                    <emph type="italics"/>
                  DS
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ds, ES
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  es,
                    <emph.end type="italics"/>
                  ) lineæ
                    <emph type="italics"/>
                  PE, PF
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  pe, pf
                    <emph.end type="italics"/>
                    <lb/>
                  & lineolæ
                    <emph type="italics"/>
                  DF, df
                    <emph.end type="italics"/>
                  pro æqualibus habeantur; quippe quarum ra­
                    <lb/>
                  tio ultima, angulis illis
                    <emph type="italics"/>
                  DPE, dpe
                    <emph.end type="italics"/>
                  ſimul evaneſcentibus, eſt æ­
                    <lb/>
                  qualitatis. </s>
                  <s>His itaque conſtitutis, erit
                    <emph type="italics"/>
                  PI
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PF
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  RI
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DF,
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  pf
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  pi
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  df
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ri
                    <emph.end type="italics"/>
                  ; & ex æquo
                    <emph type="italics"/>
                  PIXpf
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PFXpi
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  RI
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ri,
                    <emph.end type="italics"/>
                  hoc eſt (per Corol. </s>
                  <s>3. Lem. </s>
                  <s>VII,) ut arcus
                    <emph type="italics"/>
                  IH
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  arcum
                    <emph type="italics"/>
                  ih.
                    <emph.end type="italics"/>
                  Rurſus
                    <emph type="italics"/>
                  PI
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  IQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SE,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ps
                    <emph.end type="italics"/>
                  and
                    <emph type="italics"/>
                  pi
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  se
                    <emph.end type="italics"/>
                    <lb/>
                  vel
                    <emph type="italics"/>
                  SE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="iq;">ique</expan>
                    <emph.end type="italics"/>
                  & ex æquo
                    <emph type="italics"/>
                  PIXps
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PSXpi
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  IQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="iq.">ique</expan>
                    <emph.end type="italics"/>
                  ET
                    <lb/>
                  conjunctis rationibus
                    <emph type="italics"/>
                  PI quad.XpfXps
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  pi quad.XPFXPS,
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  IHXIQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="ihXiq;">ihXique</expan>
                    <emph.end type="italics"/>
                  hoc eſt, ut ſuperficies circularis, quam </s>
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